Some results on convex meromorphic functions

Faruk Ucar, Yusuf Avci

Abstract


In this paper, we define a function \(F : D\times D\times D\to \mathbb{C}\) in terms of \(f\) and show that Re\(F > 0\) for all \(\zeta,z,w \in D\) if and only if \(f\) belongs to the class of convex meromorphic functions.

Keywords


Univalent functions; convex meromorphic functions; starlike functions

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References


Duren, P. L., Univalent Functions, Springer-Verlag, Berlin–Heidelberg–New York, 1983.

Miller, J. E., Convex and starlike meromorphic functions, Proc. Amer. Math. Soc. 80 (1980), 607–613.

Gunning, R. C., Introduction to holomorphic functions of several variables, Vol. I, Function Theory, Wadsworth & Brooks/Cole, Pacific Grove – California, 1990.

Hormander, L., An introduction to complex analysis in several variables, Third Edition, North-Holland Publishing Co., Amsterdam, 1990.

Ohno, R., A study on concave functions in geometric function theory, Ph.D. thesis, Tohoku University, 2014.

Ruscheweyh, St., Sheill-Small, T., Hadamard Products of schlicht functions and the Polya–Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119–135.

Schober, G., Univalent Functions – Selected Topics, Springer-Verlag, New York–Berlin, 1975.

Sheil-Small, T., On convex univalent functions, J. London Math. Soc. 2 (1) (1969), 483–492.

Yulin, Z., Owa, S., Some remarks on a class of meromorphic starlike functions, Indian J. Pure Appl. Math. 21 (9) (1990), 833–840.




DOI: http://dx.doi.org/10.17951/a.2019.73.1.75-82
Date of publication: 2019-12-19 10:33:49
Date of submission: 2019-12-17 11:49:27


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